In this paper, two-dimensional and axisymmetric, time dependent transonic and supersonic flows over a projectile overtaking a moving shock wave are considered. The flow is simulated numerically by solving full time averaged Navier-Stokes equations. The equations are linearized by Newton approach. The roe’s flux splitting method, second order central difference scheme for the diffusion terms, and the second order approximation for time derivatives are used. For the turbulence terms, the Baldwin-Lomax and mixing length turbulence models are used. The present algorithm captures all the complicated features of flow including moving shock waves, expansion waves, boundary layers and wakes and their interactions. The results show that as the projectile passes through the moving shock wave, it changes the flow field features and pressure distribution dramatically. The drag force decreases and even becomes negative while the projectile takes over the shock wave. The flow features and the aerodynamic forces in transonic flow changes much more than those in the supersonic flow, as the projectile passes through the shock wave. The results show that when the shock wave passes though the projectile, the flow field structures and the aerodynamic forces change abruptly. The drag force reduces and the shock wave passes through the projectile. Such variations are more pronounced for transonic flows compared to the supersonic flows. For transonic flows, the drag force changes sign and accelerate of the projectile. Such behavior is important when the stability and control of the projectile is studied. Also such changes in pressure around the projectile and in the wake region change the projectile trajectory.